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Simplifying -1x2 + -30x + 108 = 0 Reorder the terms: 108 + -30x + -1x2 = 0 Solving 108 + -30x + -1x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -108 + 30x + x2 = 0 Move the constant term to the right: Add '108' to each side of the equation. -108 + 30x + 108 + x2 = 0 + 108 Reorder the terms: -108 + 108 + 30x + x2 = 0 + 108 Combine like terms: -108 + 108 = 0 0 + 30x + x2 = 0 + 108 30x + x2 = 0 + 108 Combine like terms: 0 + 108 = 108 30x + x2 = 108 The x term is 30x. Take half its coefficient (15). Square it (225) and add it to both sides. Add '225' to each side of the equation. 30x + 225 + x2 = 108 + 225 Reorder the terms: 225 + 30x + x2 = 108 + 225 Combine like terms: 108 + 225 = 333 225 + 30x + x2 = 333 Factor a perfect square on the left side: (x + 15)(x + 15) = 333 Calculate the square root of the right side: 18.248287591 Break this problem into two subproblems by setting (x + 15) equal to 18.248287591 and -18.248287591.Subproblem 1
x + 15 = 18.248287591 Simplifying x + 15 = 18.248287591 Reorder the terms: 15 + x = 18.248287591 Solving 15 + x = 18.248287591 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-15' to each side of the equation. 15 + -15 + x = 18.248287591 + -15 Combine like terms: 15 + -15 = 0 0 + x = 18.248287591 + -15 x = 18.248287591 + -15 Combine like terms: 18.248287591 + -15 = 3.248287591 x = 3.248287591 Simplifying x = 3.248287591Subproblem 2
x + 15 = -18.248287591 Simplifying x + 15 = -18.248287591 Reorder the terms: 15 + x = -18.248287591 Solving 15 + x = -18.248287591 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-15' to each side of the equation. 15 + -15 + x = -18.248287591 + -15 Combine like terms: 15 + -15 = 0 0 + x = -18.248287591 + -15 x = -18.248287591 + -15 Combine like terms: -18.248287591 + -15 = -33.248287591 x = -33.248287591 Simplifying x = -33.248287591Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.248287591, -33.248287591}
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